Rational Numbers and Square Roots

Date: 10/07/98 at 18:55:40
From: Will Chase
Subject: Rational numbers and square roots
Our teacher told us to find all the rational numbers we could
containing a sqrt symbol. To do this I could only think of sqrt4,
sqrt9, sqrt16, sqrt25, etc. Are there other things that could go
under the sqrt symbol that would be considered rational?

Date: 10/08/98 at 12:23:12
From: Doctor Peterson
Subject: Re: Rational numbers and square roots
Hi, Will -
How about 1/4, for example? Try squaring any rational number, and put
it under a sqrt!
Of course, I hope you recognize that numbers don't contain sqrts -
only representations of numbers do! Any rational number that can be
written with a sqrt can also be written without one; that's the
definition of rational.
So your sqrt(4) is really 2, and doesn't need any sqrt.
- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/